Abstract
In the algebraic Interacting Vector Boson Model (IVBM) it is assumed that the nuclear dynamics can be described by means of two types of vector “quasiparticles,” which are also characterized by another quantum number—a “T-spin” (an analogue to the F-spin). The non-compact symplectic group Sp(12, R) appears as the group of dynamical symmetry for the problem of two interacting vector bosons. The symplectic structure allows the change in the number of phonons, needed to build the collective states, that results in larger model spaces, which can accommodate the more complex structural effects as observed in the contemporary experiment. The applications of the IVBM are extended by exploiting three new subgroup chains in the reduction of Sp(12, R) to the physical angular momentum subgroup SO(3). The corresponding exactly solvable limiting cases are applied to achieve a description of complex nuclear collective spectra of even-even nuclei in the rare earth and actinide regions up to states of very high angular momentum. The first reduction that we exploit is one that extends the rotational limit of the number preserving version of the model; namely, Sp(12, R) ⊃ U(6) ⊃ U(2) ⊗ SU(3). Another limit of the symplectic IVBM, Sp(12, R) ⊃ Sp(2, R) ⊗ SO(6), contains in a natural way the 6-dimensional Davidson potential. In both of these cases, because collective modes can be mixed, we obtain successful descriptions of both positive and negative parity band configurations. The structure of band-head configurations, whose importance is established in the first two limits, is also examined in a third reduction, Sp(12, R) ⊃ Sp(4, R) ⊗ SO(3). The distributions of energies that are obtained in this limit with respect to the number of bosons that build each of the states with fixed angular momentum, enables one to distinguish typical collective vibrational and rotational spectra. This algebraic chain also provides important links between the subgroups of the other limits. The symplectic extension of the IVBM permits a richer classification of the states than its unitary version and is shown to be appropriate for a description of rather diverse nuclear spectra.
Similar content being viewed by others
References
Mitsuo Sakai, Atom. Data Nucl. Data Tabl. 31, 399 (1984); Level Retrieval Parameters, http://iaeand.iaea.or.at/nudat/levform.html; Evaluated Nuclear Structure Data File (ENSDF), http://i.e.lbl.gov/databases,endsdfserve.html.
F. Iachello and A. Arima, The Interacting Boson Model (Cambridge Univ., Cambridge, 1978).
R. F. Casten, Nucl. Phys. A 443, 1 (1985).
F. Iachello, Phys. Rev. Lett. 85, 3580 (2000); F. Iachello, Phys. Rev. Lett 87, 052502 (2001); J. Jolie et al., Phys. Rev. Lett 89, 182 502 (2002); F. Iachello, Phys. Rev. Lett. 91, 132 502 (2003).
A. Bohr and B. R. Mottelson, Nuclear Structure (Benjamin, New York, 1975).
T. Dytrych, K. D. Sviratcheva, C. Bahri, et al., Phys. Rev. Lett. 98, 162 503 (2007).
J. M. Eisenberg and W. Greiner, Nuclear Theory (North-Holland, Amsterdam, 1970), Vol. 1.
R. F. Dashenand and M. Gell-Mann, Phys. Lett 17, 142 (1965).
J. P. Elliott, Proc. R. Soc. London, Ser. A 245, 128 (1988); Proc. R. Soc. London Ser. A 245, 562 (1958).
O. Castaños, J. P. Draayer, and Y. Leschber, Z. Phys. A 329, 33 (1988).
P. Raychev, Sov. J. Nucl. Phys. 16, 1171 (1970).
P. Raychev and R. Roussev, Sov. J. Nucl. Phys. 27, 1501 (1978).
D. Karadjov, J. Piperova, P. Raychev, and R. Roussev, JINR Commun. P4-11670 (1978); D. Karadjov, P. Raychev, and R. Roussev, JINR Commun. P4-11671 (1978).
A. Georgieva, P. Raychev, and R. Roussev, J. Phys. G 8, 1377 (1982).
A. Georgieva, P. Raychev, and R. Roussev, J. Phys. G 9, 521 (1983).
A. Arima and F. Iachello, Phys. Rev. Lett. 35, 1069 (1975).
A. Arima and F. Iachello, Ann. Phys. 99, 253 (1976).
A. Arima and F. Iachello, Ann. Phys. 111, 201 (1978).
O. Castanos, E. Chacon, A. Frank, and M. Moshinsky, J. Math. Phys. 20, 35 (1961).
V. Vanagas, E. Nadjakov, and P. Raychev, Preprint IC/75/40 (ICTP, Trieste, 1975).
D. Janssen, R. V. Jolos, and F. Donau, Nucl. Phys. A 224, 93–115 (1974).
R. V. Jolos and D. Janssen, Fiz. Elem. Chastits At. Yadra 8, 330 (1977).
D. Janssen, F. Donau, S. Frauendorf, and R. V. Jolos, Nucl. Phys. A 172, 145 (1971).
M. Moshinsky, Group Theory and the Many Body Problem (Gordon and Breach, New York, 1968); M. Moshinsky, J. Math. Phys. 25, 1555 (1984).
D. J. Rowe, Prog. Part. Nucl. Phys. 37, 4711 (1995).
V. V. Vanagas, Algebraic Foundations of Microscopic Nuclear Theory (Nauka, Moscow, 1988) [in Russian].
G. Rosensteel and D. J. Rowe, Phys. Rev. Lett. 38, 10 (1977).
G. Rosensteel and D. J. Rowe, Ann. Phys. 126, 343 (1980).
W. Greiner and J. Maruhn, Nuclear Models (Springer, Berlin, Heidelberg, 1995).
T. Dytrych, K. D. Sviratcheva, C. Bahri, et al., Phys. Rev. C 76, 014315 (2007); J. Phys. G 35, 095101 (2008).
P. Navratil, J. P. Vary, and B. R. Barrett, Phys. Lett. 84, 5728 (2000); Phys. Rev. C 62, 054311 (2000).
A. Arima, M. Harvey, and K. Shimizu, Phys. Lett. B 30, 517 (1969); K. T. Hecht and A. Adler, Nucl. Phys. A 137, 129 (1969); J. P. Draayer, “Pseudospin in Perspective,” in Group Theory in Physics (Cocoyoc, Morelos, Mexico, 1991).
H. Lipkin, Nucl. Phys. A 350, 16 (1980).
V. Bargmann and M. Moshinsky, Nucl. Phys. 23, 177 (1961).
G. Rosensteel and D. J. Rowe, Int. J. Theor. Phys. 16, 63 (1977).
P. Raychev, Comp. Ran. Bulg. Acad. Sci. 25, 1503 (1972).
R. M. Asherova, V. A. Knir, Yu. F. Smirnov, and V. N. Tolstoy, Sov. J. Nucl. Phys. 21, 1126 (1975).
H. Ganev, V. Garistov, and A. Georgieva, Phys. Rev. C 69, 014305 (2004).
R. M. Asherova, D. V. Fursa, A. Georgieva, and Y. F. Smirnov, J. Phys. G 19, 1887–1901 (1993); Izv. Akad. Nauk, Ser. Phys. 56, 129–136 (1992).
G. Kyrchev and V. Paar, Ann. Phys. 170, 257 (1986).
R. V. Jolos, G. Kyrchev, and V. Paar, Fiz. Elem. Chastits At. Yadra 18, 1173 (1987).
H. G. Ganev, A. I. Georgieva, and J. P. Draayer, Phys. Rev. C 72, 014314 (2005).
H. Ganev, V. P. Garistov, A. I. Georgieva, and J. P. Draayer, Phys. Rev. C 70, 010411 (2004).
D. P. Menezes, D. M. Brink, and D. Bonatsos, Nucl. Phys. A 494, 186 (1989).
M. Moshinsky and C. Quesne, J. Math. Phys. 12, 1791 (1971).
D. A. Varshalovich, A. N. Moskalev, and V. K. Hersonsky, Quantum Theory of the Angular Momentum (Nauka, Leningrad, 1975) [in Russian].
A. Arima, T. Otsuka, F. Iachello, and I. Talmi, Phys. Lett. B 66, 205 (1977); J. P. Elliott and J. A. Evans, Phys. Lett. B 101, 216 (1981); J. P. Elliott and A. P. White, Phys. Lett. B 97, 169 (1980).
F. Iachello and I. Talmi, Rev. Mod. Phys. 59, 339 (1987).
D. J. Rowe, G. Rosensteel, and R. Carr, J. Phys. A 17, L399 (1984); J. Deenen and C. Quesne, J. Math. Phys. 23, 878 (1982); O. Castaños, E. Chacón, M. Moshinsky, and C. Quesne, J. Math. Phys. 26, 2107 (1985).
D. J. Rowe, J. Math. Phys. 27, 2662 (1984); K. T. Hecht, Lecture Notes in Physics (Springer, Berlin, 1987), Vol. 290.
A. M. Perelomov, Generalized Coherent States and Their Applications (Springer, Berlin, 1986).
F. J. Dayson, Phys. Rev. 12, 1217 (1956).
T. Holstein and H. Primakoff, Phys. Rev. 58, 1098 (1940).
D. Bonatsos and A. Klein, Phys. Rev. C 31, 992 (1985); D. Bonatsos, A. Klein, and Q. Y. Zhang, Phys. Lett. B 175, 249 (1986); D. P. Menezes and D. Bonatsos, Nucl. Phys. A 499, 29 (1989).
J. Dobaczewski, Nucl. Phys. A 369, 213 (1981); Nucl. Phys. A 369, 237 (1981); Nucl. Phys. A 380, 1 (1982).
Y. F. Smirnov, V. N. Tolstoy, A. A. Saharuk, M. Havlihceh, and C. Burdic, Group Theory Methods in Physics, Ed. by M. A. Markov (Nauka, Moscow, 1983), Vol. 2, p. 517.
Y. F. Smirnov and V. N. Tolstoy, Symmetries and Nuclear Structure, Ed. by R. A. Meyer and V. Paar (Harwood, New York, 1987), p. 24.
P. Park, Phys. Rev. C 35, 805 (1987).
J. Dobes, S. P. Ivanova, R. V. Jolos, and R. Pedrosa, Phys. Rev. C 41, 1840 (1990).
A. I. Georgieva, M. I. Ivanov, P. P. Raychev, and R. R. Roussev, Int. J. Theor. Phys. 25, 1181 (1986).
V. V. Vanagas, Algebraic Foundations of Microscopic Nuclear Theory (Nauka, Moscow, 1989) [in Russian].
A. M. Perelomov and V. S. Popov, Sov. J. Nucl. Phys. 5, 489 (1967).
H. B. Geyer, C. A. Engelbrecht, and F. J. W. Hahne, Phys. Rev. C 33, 1041 (1986).
E. Marshalek and A. Klein, Z. Phys. A 329, 44 (1989).
Wu Cheng-Li et al., Phys. Rev. C 36, 1157 (1987).
P. Halse and Z. Y. Pan, Phys. Rev. C 36, 1212 (1987).
P. Halse, J. P. Elliott, and J. A. Evans, Nucl. Phys. A 417, 301 (1984).
P. A. Butler and W. Nazarewicz, Rev. Mod. Phys. 68, 349 (1996).
R. V. Jolos, P. von Brentano, and F. Donau, J. Phys. G 19, L151 (1993); T. M. Shneidman, G. G. Adamian, N. V. Antonenko, et al., Phys. Lett. B 526, 322 (2002); T. M. Shneidman, G. G. Adamian, N. V. Antonenko, and R. V. Jolos, Phys. Rev. C 74, 034316 (2006).
J. Engel and F. Iachello, Phys. Rev. Lett 54, 1126 (1985); J. Engel and F. Iachello, Nucl. Phys. A 472, 61 (1987); V. Zamfir and D. Kusnezov, Phys. Rev. C 63, 0540 (2001).
Alonso et al., Nucl. Phys. A 586, 100 (1995).
A. A. Raduta and D. Ionescu, Phys. Rev. C 67, 044312 (2003).
A. A. Raduta, D. Ionescu, I. I. Ursu, and Amand Faessler, Nucl. Phys. A 720, 43 (2003).
A. Georgieva, P. Raychev, and R. Roussev, Bulg. J. Phys. 12, 147 (1985).
H. Ganev, V. Garistov, and A. Georgieva, in Proc. of the XXII Intern. Workshop on Nuclear Theory (Rila Mountains, Bulgaria, 2003).
D. Bonatsos, C. Daskaloyannis, S. Drenska, et al., Phys. Rev. C 62, 024301 (2000).
P. E. Garrett, J. Phys. G 27, R1–R22 (2001).
U. Kneissl et al., Phys. Rev. Lett. 71, 2180 (1993).
J. P. Draayer, “Algebraic Approaches to Nuclear Structure: Interacting Boson and Fermion Models,” in Contemporary Concepts in Physics VI, Ed. by Casten R. F. Chur (Harwood Academic, Switzerland, 1993), p. 423.
G. Popa, A. Georgieva, and J. P. Draayer, Phys. Rev. C 69, 064307 (2004).
Y. Leshber and J. P. Draayer, Phys. Lett. B 190, 1 (1987); O. Castaños, J. P. Draayer, and Y. Leshber, Z. Phys. A 329, 33 (1988).
R. F. Casten and N. V. Zamfir, Phys. Rev. Lett. 85, 3584 (2000); M. A. Caprio, “Experiments on Critical Point Nuclei-Mapping the Triangle,” AIP Conf. Proc. 638, 17 (2002).
A. A. Solnishkin, V. P. Garistov, A. Georgieva, H. Ganev, and V. V. Burov, Phys. Rev. C 72, 0643321 (2005).
J. Adam et al., BRAS Phys. 66, 1384 (2002); A. Jungclaus et al., Phys. Rev. C 66, 014312 (2002).
H. G. Ganev and A. I. Georgieva, Phys. Rev. C 76, 054322 (2007).
S. Alisauskas, A. Georgieva, P. Raychev, and R. Roussev, Bulg. J. Phys. 11, 150 (1984).
G. Racah, Phys. Rev. 76, 1352 (1949).
N. Matagne and F. Stancu, Phys. Rev. D 73, 114 025 (2006).
J. P. Draayer and Y. Akiyama, J. Math. Phys. 14, 1904 (1973).
D. Vergados, Nucl. Phys. A 111, 681 (1968).
B. G. Wybourne, Classical Groups for Physicists (Wiley, New York, 1974); C. Quesne, J. Phys. A 03, 847 (1990); J. Phys. A 04, 0697 (1991).
K. T. Hecht, R. Le Blanc, and D. J. Rowe, J. Phys. A 20, 2241 (1987).
R. Le Blanc and D. J. Rowe, J. Phys. A 20, L681 (1987).
D. J. Rowe, R. Le Blanc, and J. Repka, J. Phys. A 22, L309 (1989).
H. Ower et al., Nucl. Phys. A 388, 421 (1982); S. Kuyucak and S. C. Li, Phys. Lett. B 354, 189 (1995).
M. R. Schmorak, Nucl. Data Sheets 63, 183 (1991).
P. M. Davidson, Proc. Roy. Soc. A 135, 459 (1932).
D. J. Rowe, J. Math. Phys. 35, 3178 (1994); D. J. Rowe and C. Bahri, J. Phys. A 31, 4947 (1998).
M. Moshinsky and C. Quesne, J. Math. Phys. 11, 1631 (1970); J. Math. Phys. 12, 1772 (1971).
M. Moshinsky, J. Math. Phys. 25, 1555 (1984).
Feng Pan and J. P. Draayer, Nucl. Phys. A 636, 156 (1998).
E. Chacon, O. Castaños, and A. Frank, J. Math. Phys. 25, 1442 (1984).
A. J. Dragt, J. Math. Phys. 6, 533 (1965).
J. P. Elliott, J. A. Evans, and P. Park, Phys. Lett. B 169, 309 (1986); J. P. Elliott, P. Park, and J. A. Evans, Phys. Lett. B 171, 145 (1986).
H. G. Ganev, A. I. Georgieva, and J. P. Draayer, “Transitional Nuclear Spectra within the Framework of Interacting Vector Boson Model with 6-Dimensional Davidson Potential,” in Proc. of the XXIV Intern. Workshop on Nuclear Theory, Ed. by S. Dimitrova (Heron Press Sci. Ser., Sofia, 2005), p. 169.
D. Tonev et al., Phys. Rev. C 69, 034334 (2004).
R. M. Clark et al., Phys. Rev. C 69, 064322 (2004); A. I. Georgieva, Tz. Venkova, and A. Aprahamian, “Systematics of Nuclei with Critical Point Symmetries in the Rare Earth Region,” in Proc. of the XXIII Intern. Workshop on Nuclear Theory, Ed. by S. Dimitrova (Heron Press Sci. Ser., Sofia, 2004), pp. 283–294.
V. Garistov, “Rearrangement of the Experimental Data of Low Lying Collective Excited States,” in Proc. of the XXII Intern. Workshop on Nuclear Theory, Ed. by V. Nikolaev (Heron Press Sci. Ser., Sofia, 2003), p. 305.
V. Garistov, “On Description of the Yrast Lines in IBM-1,” in Proc. of the XXI Intern. Workshop on Nuclear Theory, and Ed. by V. Nikolaev (Heron Press Sci. Ser., Sofia, 2002).
D. J. Rowe, Phys. Rev. Lett. 93, 122 502 (2004).
Author information
Authors and Affiliations
Additional information
The article is published in the original.
Rights and permissions
About this article
Cite this article
Georgieva, A.I., Ganev, H.G., Draayer, J.P. et al. Description of mixed-mode dynamics within the symplectic extension of the Interacting Vector Boson Model. Phys. Part. Nuclei 40, 461–501 (2009). https://doi.org/10.1134/S1063779609040029
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063779609040029